Cation Disorder and Large Tetragonal Supercell Ordering in the Li-Rich Argyrodite Li7Zn0.5SiS6

A tetragonal argyrodite with >7 mobile cations, Li7Zn0.5SiS6, is experimentally realized for the first time through solid state synthesis and exploration of the Li–Zn–Si–S phase diagram. The crystal structure of Li7Zn0.5SiS6 was solved ab initio from high-resolution X-ray and neutron powder diffraction data and supported by solid-state NMR. Li7Zn0.5SiS6 adopts a tetragonal I4 structure at room temperature with ordered Li and Zn positions and undergoes a transition above 411.1 K to a higher symmetry disordered F43m structure more typical of Li-containing argyrodites. Simultaneous occupation of four types of Li site (T5, T5a, T2, T4) at high temperature and five types of Li site (T5, T2, T4, T1, and a new trigonal planar T2a position) at room temperature is observed. This combination of sites forms interconnected Li pathways driven by the incorporation of Zn2+ into the Li sublattice and enables a range of possible jump processes. Zn2+ occupies the 48h T5 site in the high-temperature F43m structure, and a unique ordering pattern emerges in which only a subset of these T5 sites are occupied at room temperature in I4 Li7Zn0.5SiS6. The ionic conductivity, examined via AC impedance spectroscopy and VT-NMR, is 1.0(2) × 10–7 S cm–1 at room temperature and 4.3(4) × 10–4 S cm–1 at 503 K. The transition between the ordered I4 and disordered F43m structures is associated with a dramatic decrease in activation energy to 0.34(1) eV above 411 K. The incorporation of a small amount of Zn2+ exercises dramatic control of Li order in Li7Zn0.5SiS6 yielding a previously unseen distribution of Li sites, expanding our understanding of structure–property relationships in argyrodite materials.


INTRODUCTION
The argyrodite family of materials, related to the mineral Ag 8 GeS 6 , exhibit considerable compositional flexibility and have been extensively studied for various applications including fast ion conduction (e.g., Ag 7 GeSe 5 I and Cu 6 PS 5 Cl), 1,2 thermoelectrics (e.g., Cu 8 GeS 6 and Ag 8 SnSe 6 ), 3,4 and nonlinear optical (Cd 3.25 PS 5.5 I 0.5 ) materials. 1 The degree of structural disorder, which can be controlled through cationic or anionic substitution, determines the properties of argyrodite materials, so reliable characterization of such crystal structures is critical to expanding our knowledge of these systems. 5 The crystal structures of argyrodites such as Li 6 PS 5 X (X = Cl, Br) have tetrahedral close packed topologies related to that of the Laves phases (e.g., MgCu 2 ) with high symmetry aristotype argyrodite polymorphs adopting cubic F43m symmetry. 1 Recently, we demonstrated that the argyrodite structure can also be considered equivalent to that of antiperovskite through anion and vacancy ordering within a cubic stacking of two closepacked layers that enabled the discovery of a hexagonal argyrodite Li 6 SiO 4 Cl 2 . 6 The argyrodite Li 6 MS 4 XX′ structure can be described for sulfides as a cubic close-packed arrange-ment of MS 4 tetrahedral polyanions (where M can be Si 4+ , P 5+ , Ge 4+ , etc.) with individual X and X′ anions (X/X′ = S 2− , O 2− , Cl − , Br − , I − ) occupying the octahedral and half of the tetrahedral voids, respectively, as shown in Figure 1a. This generates five distinct types of tetrahedral void (Figure 1b) that can be occupied by Li + cations, 5,7,8 and in high symmetry F43m argyrodite structures, the Li + cations can be ordered such as in Li 6 PO 5 X (X = Cl, Br) or dynamically disordered as observed in Li 6 PS 5 X (X = Cl, Br). 9,10 This dynamic disorder is manifested with Li + ions delocalized across several lattice positions (commonly, the 24g and 48h Wyckoff sites frequently referred to as T5a and T5 sites, respectively), 5 which leads to reduced activation barriers for ion mobility in these systems, with Li 6 PS 5 Br exhibiting an ionic conductivity of 6.8 × 10 −3 S cm −1 at room temperature. 11 In contrast, despite adopting F43m symmetry, Li 6 PO 5 Br has a room-temperature conductivity of ∼10 −9 S cm −1 , which results from statically ordered Li + positions on the 24g (T5a) site, and an order−disorder transition is not observed for Li 6 PO 5 Br in the temperature range of 173−873 K. 10 Dynamic Li + disorder leading to superionic performance is common in mixed sulfide/halide argyrodites such as Li 6 PS 5 X (X = Cl, Br) in which a high degree of sulfide/halide disorder modifies the anionic charge distribution, leading to significantly delocalized lithium positions, 5,12 and also in mixed cation materials such as Li 6+x Sb 1−x Sn x S 5 I and Li 6+x P 1−x Si x S 5 Br where aliovalent substitution increases Li + carrier concentration and creates high-energy interstitial sites that participate in Li + diffusion. 13,14 Lower symmetry argyrodite polymorphs are stabilized when the Li + cations are ordered, as in Li 7 PCh 6 (Ch = S, Se), which adopt orthorhombic Pna2 1 symmetry at room temperature and are isostructural to α-Cu 7 PSe 6 . 7,15,16 Both Li 6 PS 5 I and Li 6 AsS 5 I adopt Cc symmetry at temperatures below 180 and 173 K, respectively, and are isostructural to Cu 6 PS 5 Br with full Li + occupancy of either tetrahedral (T5) or trigonal planar (T5a) sites (4a Wyckoff sites in Cc) to yield ordered positions. 7,17 These orthorhombic (Pna2 1 ) and monoclinic (Cc) symmetries are subgroups of F43m, and the materials exhibit a transition to cubic higher symmetry disordered structures with significant enhancement in ion transport above these temperatures. In the high symmetry (F43m) structures, Li + ions are disordered with partial occupancies of tetrahedral (48h, T5) positions for Li 7 PCh 6 (Ch = S, Se) and Li 6 AsS 5 I and both tetrahedral (48h, T5) and trigonal (24g, T5a) positions for Li 6 PS 5 I. Three other structural symmetries are commonplace in non-Li argyrodite materials: orthorhombic Pmn2 1 as observed for Cu 8 SiCh 6 (Ch = S and Se), hexagonal P6 3 cm (e.g., for Cu 8 GeS 6 ), and cubic P2 1 3 as adopted by Ag 7 PS 6 and Cu 7 PS 6 . 1, 3 Here, we report the discovery and synthetic isolation of new Li 7 Zn 0.5 SiS 6 as the first argyrodite material reported with a tetragonal (I4) crystal structure. A reversible transition is observed through differential scanning calorimetry and variable temperature X-ray and neutron powder diffraction above 411 K where Li 7 Zn 0.5 SiS 6 exhibits a disordered cubic F43m structure analogous to other argyrodites that leads to a significant decrease in activation energy for Li + ion transport to 0.34(1) eV from 0.66(1) eV for the ordered room-temperature I4 structure. Zn 2+ cations occupy a single lattice site in the F43m structure shared with Li + , but only a small subset of these sites is occupied by Zn 2+ at room temperature in the I4 structure. This addition of a small amount of Zn 2+ drives the Zn and Li ordering to generate the lower symmetry tetragonal I4 structure at room temperature. Ionic conductivity is measured via AC impedance spectroscopy and Li + ion mobility assessed via NMR as a local probe.

EXPERIMENTAL SECTION
2.1. Exploratory Synthesis in the LiS 0.5 -ZnS-SiS 2 Phase Field. All reagents and samples were handled under inert helium atmosphere (O 2 < 1 ppm). Solid state reactions were carried out by flame sealing reagent mixtures (typically, 300 mg for each reaction) inside carboncoated evacuated quartz ampules (<10 −4 mbar). Stoichiometric mixtures of lithium sulfide (Li 2 S, Sigma-Aldrich, 99.98%), zinc sulfide (ZnS, Sigma-Aldrich, 99.99%), silicon powder (Si, Alfa Aesar, 325 mesh, 99.5%), and elemental sulfur (S, Sigma-Aldrich, 99.999%) were used as provided and thoroughly ground for 15 min using an agate pestle and mortar. For initial exploratory reactions in the LiS 0.5 -ZnS-SiS 2 phase field, these reaction mixtures were heated to 673 K at a heating rate of 5 K min −1 , then heated to 973 K at a slower rate of 0.5 K min −1 , and held at 973 K for 24 h before being cooled to ambient temperature at a rate of 5 K min −1 . Resulting powders were ground Chemistry of Materials pubs.acs.org/cm Article before being fired again to 973 K for 24 h using a heating and cooling rate of 5 K min −1 . Li 7 Zn 0.5 SiS 6 . Powders of Li 7 Zn 0.5 SiS 6 were obtained using stoichiometric mixtures of the above starting materials sealed in carbon-coated evacuated quartz ampules, which were fired to 973 K for 24 h using a heating and cooling rate of 5 K min −1 twice with the powders ground in between the two firings. This reaction procedure yielded phase pure samples of Li 7 Zn 0.5 SiS 6 as assessed by laboratory powder X-ray diffraction (PXRD) data.

Synthesis of
2.3. Powder Diffraction. Routine PXRD analysis of phase purity and lattice parameters was performed on a Bruker D8 Advance diffractometer with a monochromatic Cu X-ray source (Kα 1 , λ = 1.54056 Å) or Mo X-ray source (Kα 1 , λ = 0.70932 Å) in Debye− Scherrer geometry. Powder samples were sealed inside borosilicate glass capillaries. Structure determination and Rietveld refinements were carried out on synchrotron X-ray diffraction (SXRD) data collected at the I11 beamline (Diamond Light Source, U.K.) with an incident wavelength of 0.824878(10) Å. High-resolution data were collected at room temperature using the multianalyzer crystal (MAC) detectors. Samples were sealed inside Ø = 0.3 mm borosilicate capillaries. Variable temperature SXRD measurements from ambient temperature to 448 K in 25 K steps were carried out on beamline I11 using an Oxford Cryostream Plus with the Mythen position sensitive detector (PSD). Data were collected on heating using a heating and cooling rate of 10 K min −1 .
Time-of-flight neutron powder diffraction (NPD) data were collected at ambient temperature (300 K) and at 448 K using the low temperature furnace on the Polaris instrument at ISIS, the U.K. spallation neutron source. Powders were loaded into thin-walled vanadium metal cans of 6 mm diameter under an inert helium atmosphere and sealed using a copper gasket. Data were collected on a 7 Li enriched sample to minimize the impact of absorption using a 7 Li 2 S precursor, which was synthesized from 7 Li 2 CO 3 (Sigma-Aldrich, 99%) that was heated to 923 K under flowing CS 2 vapor for 6 h. 18 2.4. Elemental Analysis. Elemental analysis of Li 7 Zn 0.5 SiS 6 was carried out by Mikroanalytisches Labor Pascher (Remagen-Bandorf, Germany). The powder was dissolved, and elements were detected by inductively coupled plasma atomic emission spectroscopy (ICP-AES) using a Thermo Fisher Scientific iCap 6500 instrument.
2.5. Differential Scanning Calorimetry (DSC). Heat flux profiles were measured from 17 mg of powdered sample in a 100 μL Ni/Cr crucible sealed under a helium atmosphere (O 2 < 1 ppm) using a Netzsch DSC 404 F1 differential scanning calorimeter. Data were recorded on heating from 303 to 773 K and then cooling to 303 K using a heating and cooling rate of 1 K min −1 under a constant 50 mL min −1 flow of helium. The temperature of the observed transition is the average of the values obtained from both the heating and cooling data sets, which were extracted through peak fitting.
2.6. Raman Spectroscopy. Raman spectra were collected on samples sealed under a helium atmosphere in borosilicate glass capillaries (O 2 < 1 ppm) using an inVia Reflex Qontor Confocal Raman Microscope from Renishaw with a laser excitation wavelength of 523 nm.
2.7. Alternating Current (AC) Impedance Spectroscopy and Direct Current (DC) Polarization. A pellet of Li 7 Zn 0.5 SiS 6 was prepared by uniaxially pressing ∼30 mg of materials with a 5 mm cylindrical steel die at a pressure of 125 MPa and subsequent sintering at 923 K for 14 h using heating and cooling rates of 5 K min −1 . Using this method, a density of 81% was achieved. The pellet faces were sputtered with gold, which were used as ion-blocking electrodes. Temperature dependent AC-impedance measurements were carried out by heating the sample from 303 to 503 K in an Ar-filled glovebox (O 2 < 1 ppm, H 2 O < 1 ppm) at a rate of 3 K min −1 . Measurements were recorded in 20 K steps following a 10 min equilibration period at each target temperature. Impedance data were recorded using a Keysight Impedance Analyzer E4990A. A sinusoidal amplitude of 50 mV was employed in the frequency range of 100 MHz to 100 mHz. Impedance data were fitted with an equivalent circuit using the program ZView2. 19 The same pellet used for AC impedance measurements was used for DC polarization measurements. DC polarization data were collected at ambient conditions on an Au|Li 7 Zn 0.5 SiS 6 |Au symmetric cell using potentiostatic polarization measurements between 0.05 and 1.0 V for 2 h and monitoring the current variation with time using an Autolab 84515 instrument.
2.8. Nuclear Magnetic Resonance (NMR). 6 Li and 29 Si magic angle spinning (MAS) NMR experiments were recorded at room temperature on a 9.4 T Bruker DSX spectrometer equipped with a 4 mm HXY MAS probe (in double resonance mode) with the X channel tuned to 6 Li at ω 0 /2π( 6 Li) = 59 MHz or 29 Si at ω 0 /2π( 29 Si) = 79.5 MHz. 90°pulses of duration 3 μs at a radiofrequency (rf) amplitude of ω 1 /2π = 83 kHz were used. The MAS frequency ω r /2π was set to 10 kHz. All spectra were obtained under quantitative recycle delays of more than 5 times longer than the respective longitudinal relaxation times T 1 measured through the saturation recovery pulse sequence, and the data were fitted with a stretch exponential function in the form of 1 − exp[−(τ/T 1 ) α ] (with α values of 0.9 for the 6 Li and 29 Si data sets).
Static 7 Li variable temperature (VT) NMR experiments on a sample sealed in a glass ampule were recorded on a 9.4 T Bruker Avance III HD spectrometer equipped with a 4 mm HXY MAS probe (in double resonance mode) with the X channel tuned to 7 Li at ω 0 /2π( 7 Li) = 156 MHz. All 7 Li NMR spectra were recorded with a 90°pulse at rf field amplitude of ω 1 /2π = 83 kHz and under quantitative recycle delays of more than 5 times longer than the T 1 time measured through the saturation recovery pulse sequence with data also fitted to the same stretch exponential function as above (with α ranging from 0.8 to 0.95). The stretch exponential was used in order to account for any distribution of correlation times and temperature gradients across the sample.
The temperature calibration of the probe was carried out using the 207 Pb NMR chemical shift thermometer Pb(NO 3 ) 2 . 20 The temperature standard error associated with this method arises from the temperature gradients across the sample, which ranged from 2 to 8 K.

RESULTS AND DISCUSSION
3.1. Synthesis and Isolation of New Li 7 Zn 0.5 SiS 6 . The LiS 0.5 −ZnS−SiS 2 phase field was explored using solid state methods with reagent mixtures sealed inside the carbon-coated evacuated quartz ampules (<10 −4 mbar). Syntheses were carried out within a range of reaction temperatures (873−973 K) with all starting materials and resulting powders handled under an inert helium atmosphere (O 2 < 1 ppm). First, a selection of compositions within the phase field were synthesized, and the resulting phases were carefully matched to known materials through analysis of PXRD data (Figure 2a, red points). The majority of the synthesized compositions contained mixtures of binary sulfides and Li 2 ZnSiS 4 , which is the only quaternary that has been previously characterized within the LiS 0.5 −ZnS−SiS 2 phase field. 21 7.07(2) Zn 0.472(2) Si 1.068(6) S 6.00(6) measured by ICP-AES (Table  S1) agrees well with the expected composition of Li 7 Zn 0.5 SiS 6 and confirms that there is no loss of reagents through the reaction with the carbon-coated quartz ampule. The structure of this new phase was determined through the analysis of synchrotron X-ray diffraction (SXRD) and neutron powder diffraction data (NPD) described in detail in the following sections. All of the reflections observed for new Li 7 Zn 0.5 SiS 6 can be indexed to a tetragonal unit cell at room temperature with lattice parameters a = b ≈ 21 Å and c ≈ 10 Å with systematic absences that are consistent with the I − − − diffraction symbol ( Figure S5). High-resolution SXRD data were collected on Li 7 Zn 0.5 SiS 6 powder in the temperature range of 298−448 K in 25 K steps. Above 423 K, the convergence of some peaks and disappearance of many small peaks associated with the tetragonal lattice indicate a phase transition to a highersymmetry structure takes place (Figures S5 (inset) and S6). This transition, observed by powder diffraction, is consistent with differential scanning calorimetry (DSC) data, which show a single endothermic and exothermic thermal event at 411.1(5) K observed on heating and cooling, respectively, highlighting that the transition is reversible (Figure 2c). The peaks in the powder pattern of Li 7 Zn 0.5 SiS 6 measured at >423 K can be indexed to a cubic unit cell with a = 10.04444(3) Å and space group symmetry F43m ( Figure S5), which is similar to those observed for argyrodite materials. It is not possible to stabilize the hightemperature F43m structure of Li 7 Zn 0.5 SiS 6 to room temperature through quenching. This yields tetragonal (I4) Li 7 Zn 0.5 SiS 6 and Li 4 SiS 4 as a secondary phase ( Figure S7).
3.2. Structure Determination. 3.2.1. Determination of Li 7 Zn 0.5 SiS 6 High-Temperature Structure. The high-temperature F43m structure of Li 7 Zn 0.5 SiS 6 was obtained from the combined refinement of SXRD and NPD data, fitted using TOPAS Academic. 22 The structure of Li 6 PS 5 Br (space group F43m with approximate lattice parameter of a ≈ 10.04 Å) was used as the starting point 9 with P substituted for Si on the 4b Wyckoff site and Br substituted for S on the anion positions. The lattice parameter, background, and peak shapes were refined via the Le Bail method and then fixed throughout until the final refinement. Two Li sites (48h T5 and 24g T5a) were present in the starting model. Compared against the nominal composition of Li 7 Zn 0.5 SiS 6 , this structure is missing 1.5 cations (1 Li + and 0.5 Zn 2+ ). Three additional tetrahedral Li sites were suggested from a Fourier difference map generated using NPD data from Bank 3 of Polaris with the initial model and profile parameters from the Le Bail fit. The Li site occupancies were initially set such that the total Li content within the model was equal to 7.5 from five sites (four tetrahedra and one trigonal planar). The four tetrahedral sites were duplicated for Zn and set to an initial occupancy of zero. The site distribution of Li/Zn within the structural model was then refined using the automatic simulated annealing algorithm in TOPAS, refining for 100 000 cycles. During the simulated annealing, only the occupancies of the Li/Zn sites were allowed to vary, and the refinement was subject to a global composition restraint set by the nominal composition (Li 7 Zn 0.5 SiS 6 ). The simulated annealing resulted in Zn located on the 48h (T5) site only with Li occupying the 48h (T5), 24g (T5a), 48h (T2), and 16e (T4) sites. The fifth candidate tetrahedral site was refined to an occupancy of zero, so it was removed from the refinement. These results from simulated annealing were then used as the basis for a Rietveld refinement in which all structural parameters and profile parameters were refined. During this final refinement, the results of which are  Table 1, the global composition restraint was still used, and soft restraints were applied to the Si−S and Li−S distances of 2.1(1) and to 2.5(1) Å, respectively. These values were based on the averages if both distances were freely refined, while corresponding to sensible Si−S and Li−S distances as found in other argyrodites. 13 The final refinement resulted in the unit cell parameter a = 10.04444(3) Å and composition of Li 7.00(12) Zn 0.497(6) SiS 6 , which is in good agreement with the composition of Li 7.07(2) Zn 0.472(2) Si 1.068(6) S 6.00(6) determined analytically from ICP-AES analysis (Table S1). Though many Cu and Ag argyrodites exist with high mobile cation content (e.g., Cu 8 GeS 6 and Ag 8 SnSe 6 ), 3,4 comparatively few Li argyrodites with such a high occupancy of the mobile cation sites exist. 3.2.2. Determination of Li 7 Zn 0.5 SiS 6 Room-Temperature Structure. In principle, it should be possible to solve the roomtemperature ordering of Li 7 Zn 0.5 SiS 6 by creating the corresponding supercell of the high-temperature structure using ISODISTORT 23,24 and then performing a Rietveld refinement.
However, this generates a supercell containing 77 unique Li/Zn sites, 3 Si sites, and 15 S sites (a total of 95 sites). Consequently, solving the room-temperature structure via this route was impractical, as preliminary refinement attempts immediately indicate that the majority of the potential Li/Zn sites are not occupied at room temperature; therefore, the determination of which sites were occupied by Li and Zn starting from all possible sites would be less efficient compared to resolving through the method described below.
To solve the room-temperature structure of Li 7 Zn 0.5 SiS 6 , the unit cell was first indexed using the autoindexing function in GSAS-II with the SXRD data, 25 which resulted in the unit cell indexed as tetragonal with approximate lattice parameters a = b ≈ 21 Å and c ≈ 10 Å and systematic absences which are consistent with the I − − − diffraction symbol. This approximate unit cell was then used as the basis for a Le Bail refinement in Jana2006. 26 For the Le Bail fit, the space group was set to P1 and the background, peak profile, the six unit cell parameters, and zero error were then refined. The "make space group test" function within Jana2006 was used to suggest (d−f) Rietveld refinement against SXRD and NPD Bank 3 and Bank 5 data at 300 K using the room-temperature structural model of Li 7 Zn 0.5 SiS 6 with I4 symmetry. Traces I obs (black circles), I calc (red line), and I obs − I calc (gray line) and Bragg reflections are shown (black tick marks for Li 7 Zn 0.5 SiS 6 , green for V metal, blue for Li 2 S, pink for Li 4 SiS 4 ). The high-temperature refinement has R wp = 3.58% and χ 2 = 38.2 for 109 refined parameters, and the room-temperature refinement has R wp = 5.60% and χ 2 = 14.8 for 245 refined parameters. Chemistry of Materials pubs.acs.org/cm Article possible space groups with a tolerance of 0.02 Å on the a, b, and c unit cell parameters and 0.2°on the unit cell angles and was combined with the HKL table from the Le Bail fit to suggest possible space groups, which typically returns the highest symmetry space group from the best fitting diffraction symbol. The best achieved fit was to the space group I4m2, consistent with I − − −. The initial structure was solved using SUPERFLIP 27,28 as implemented in Jana2006. The best solutions from this method can often be achieved by starting with the lowest symmetry space group allowed by the I − − − diffraction symbol. As such, the structure solution was started in space group I4, and SUPERFLIP with its own symmetry determination is able to suggest higher symmetry solutions, where appropriate, although none that yielded a solution with an improved fitting parameter were found. The solution from SUPERFLIP using the results from a Le Bail fit in I4 symmetry against SXRD data yielded a structure containing 15× S, 3× Si, and 12× mixed Li/Zn sites and retained the I4 symmetry. This model was refined using the Rietveld method in Jana2006 against the SXRD data, allowing the occupancies of the mixed Li/Zn sites to be refined while restricting each total site occupancy to one, resulting in a structural model with an approximate composition of Li 4.55 Zn 0.5 SiS 6 . This indicated a significant amount of Li that was unaccounted for in the structure. In this model, no further sites could be located using Fourier difference mapping against the SXRD data, and due to the large difference between the model and nominal composition of Li 7 Zn 0.5 SiS 6 , it was concluded that the additional Li was likely distributed across several partially occupied sites.
To locate further Li sites within the structure, the structure derived above was refined in TOPAS academic to create an equivalent starting point and NPD data were now included in the refinement. Computing Fourier difference maps against the NPD data from Bank 3 of Polaris did not locate any additional Li sites. We repeated the following process until no new sites could be located: an additional Li/Zn site was included in the structure with randomly generated (within TOPAS) fractional coordinates with the total occupancy of the site restricted to one; this updated model is then refined using the Rietveld method for at least 10 000 refinement cycles, and each time the refinement converged, the coordinates of the new site were re-randomized (the rest of the structure and profile parameters continue to be refined as normal). Then, the solution with the lowest R wp fit parameter is carried forward. This process resulted in the location of an additional four Li sites, bringing the approximate composition to Li 7 Zn 0.5 SiS 6 in line with the nominal composition.
At this stage, the restriction of all Li/Zn sites having a total occupancy of one led to a number of nonphysical M−M The original restriction that maintained Li/Zn site occupancies to equate to one was changed such that the occupancy contribution on any given Li/ Zn site could not fall below zero. With these restrictions in place, simulated annealing was used in TOPAS for at least 100 000 refinement cycles using its automatic temperature regime, allowing only the occupancies of the Li/Zn sites to be refined. After each simulated annealing run, further Li sites were trialed in the structure as outlined previously. With the addition of each new Li/Zn site, the constraints on the occupancy of the neighboring Li/Zn sites were updated and the simulated annealing stage repeated. This process introduced an additional five Li/Zn sites into the structure at which point the composition of the model was stable and no new sites could be located (i.e., no new Li/Zn sites could be introduced that had total refined occupancies greater than one estimated standard deviation above zero). The refined composition of the model at this stage was Li 6.85(10) Zn 0.470(6) SiS 6 .
To achieve the final refinement model, distance restraints were used for the Si−S and Li/Zn−S bonds. Si−S distances were constrained softly to 2.1(±0.1) Å, while for Li/Zn−S bonds, the distance was constrained to 2.5(±0.1) Å. These values were based on the averages if distances were freely refined, while simultaneously corresponding to sensible Si−S and Li−S distances as found in other argyrodites. 13 Additionally, a soft global composition restraint, set to the nominal composition of   29 Si MAS NMR spectrum of Li 7 Zn 0.5 SiS 6 measured at 300 K. A larger spectral width covering the Q n region is shown in Figure S12. The anion sublattice of the (e) high-temperature F43m structure and (f) room-temperature I4 structure of Li 7 Zn 0.5 SiS 6 . The black lines represent the unit cell edges, and the red lines highlight the relationship between the two structures. Small orange arrows in (f) emphasize the displacements of the two 8g positions (equivalent to the 4a position in the high-temperature F43m structure) away from the center of the octahedral voids formed from the SiS 4 4− cubic close-packing.
Chemistry of Materials pubs.acs.org/cm Article which 6 contain Zn, 3× Si sites, and 15× S sites, and are discussed in detail below.  6 Li + cations are dynamically disordered across four distinct crystallographic sites in the high-temperature structure of Li 7 Zn 0.5 SiS 6 and can be represented by viewing Friauf polyhedra formed from the four SiS 4 4− polyanions that are centered around the 4c S 2− position ( Figure 4). The 48h (T5) and 24g (T5a) positions are occupied with 0.405(8) and 0.099(7) Li, respectively, accounting for most of the Li. Despite having a comparable ionic radius to Li + (tetrahedral r Li + = 0.59 Å and r Zn 2+ = 0.6 Å), 30 Zn 2+ occupies only one site in the hightemperature structure, which is the 48h (T5) site with an occupancy of 0.0414(5) Zn, giving an overall cation occupancy of 0.99(2) across the T5 and T5a sites (Figure 4b,c). The remaining Li occupies the 16e (T4) and 48h (T2) positions with occupancies of 0.243(6) and 0.048(5), respectively ( Figure  4b,c). These additional (T4 and T2) positions are sites that are less frequently occupied than the T5 and T5a sites in most Licontaining argyrodites; however, they have been observed in several other systems such as Li 6+ x Sb 1 − x Sn x S 5 I, 1 32 and Li 6 PS 5 X (X = Cl and Br) from the analysis of high-resolution neutron diffraction data, 33 and the simultaneous occupation of T5, T5a, T2, and T4 sites was very recently reported in Li 6.6 P 0.4 Ge 0.6 S 5 I. 34 The 48h (T5) tetrahedra share two corners with the SiS 4 4− polyanions with the other two corners formed by the S 2− 4c and 4a positions. A small amount of Li + (0.099 (7)) is delocalized onto the 24g (T5a) site, which lies in between the 48h (T5) positions, yielding a trigonal planar environment (Figure 4b,c). The 48h (T2) position acts as an interstitial site between adjacent 48h (T5) positions forming tetrahedra that face share with T5 sites and share edges with the SiS 4 4− polyanions. The 16e (T4) sites also share faces with the adjacent 48h (T5) tetrahedra and share edges with the 48h (T2) tetrahedra. As such, all four faces of the 48h (T5) tetrahedral environment in the average high-temperature structure of Li 7 Zn 0.5 SiS 6 are shared with other tetrahedral environments  Li + positions centered around the 4d S 2− /X − site, whereas the T4 site is located between these cages; both the T2 and T4 sites are known to play an important role in the formation of ionic diffusion pathways throughout the argyrodite structure, which will be discussed in Section 3.4.  (Table S2). There are three distinct Si 4+ positions (one 2b and two 8g), which give three types of SiS 4 4− tetrahedra. The tetrahedra in the roomtemperature I4 structure are distorted slightly from the regular tetrahedra of the high-temperature  Tables S3−S6). Though slightly irregular, these distances and angles of the tetrahedra are similar enough such that different environments are not spectroscopically resolved by 29 Si MAS NMR (Figure 5d). A single sharp resonance characteristic of SiS 4 tetrahedra 35−37 is observed at 8 ppm in the NMR spectrum of Li 7 Zn 0.5 SiS 6 , highlighting the similarity of the SiS 4 4− tetrahedra in the roomtemperature I4 structure. This is also consistent with the measured Raman spectrum of Li 7 Zn 0.5 SiS 6 ( Figure S10), which shows modes characteristic of SiS 4 4− tetrahedra at frequencies comparable to those observed for Cu 8 MCh 6 (M = Si, Ge and Ch = S, Se). 38 The S 2− anions that occupy the 4a and 4c positions in the high-temperature F43m structure occupy the 2a and two 8g and the 2d and two 8g positions, respectively, in the roomtemperature I4 structure. The 2d and two 8g positions (equivalent to the 4c position in the high-temperature F43m structure) occupy the center of half of the tetrahedral holes formed by the cubic closed-packed SiS 4 4− sublattice. The 2a and two 8g positions (equivalent to the 4a position in the hightemperature F43m structure) occupy the octahedral voids formed from the SiS 4 4− cubic close-packing; however, the S 2− anions on the two 8g positions are displaced away from the octahedral center in the room-temperature I4 structure by 0.199 (8) and 0.377(9) Å compared to the high-temperature F43m structure (Figures 5e,f and S11). The sulfide anions are displaced toward the neighboring sites, which are occupied by both Li and Zn and away from the sites partially occupied with Li, likely increasing valence and bonding for the former sites ( Figure S11).
In the room-temperature I4 structure of Li 7 Zn 0.5 SiS 6 , there are 22 crystallographically distinct Li positions (Table S2): 14 × T5, 4 × T2, 2 × T4, 1 × T1, and 1 trigonal planar (denoted as T2a) position, which has not been observed in argyrodites before. The latter two positions (T1 and T2a) are not occupied in the hightemperature F43m structure. These positions are represented in three separate Friauf polyhedra shown in Figure 6, which are formed from four SiS 4 4− polyanions that center around S 2− anions on the 2d and two 8g positions (4c in the hightemperature F43m structure). Zn occupies the 48-fold T5 site at high temperature in F43m Li 7 Zn 0.5 SiS 6 ; therefore, any of the T5 sites in I4 Li 7 Zn 0.5 SiS 6 can be occupied by Zn. However, only a subset of the T5 sites in the room-temperature I4 structure are occupied by Zn. Six of the 14 T5 sites (48h position in hightemperature F43m structure) are occupied by both Li + and Zn 2+ , the smallest and largest Zn occupancies being 0.031(5) and 0.473(4), respectively. These six T5 sites are the only positions that are occupied by Zn in the room-temperature I4 structure of Li 7 Zn 0.5 SiS 6 . Almost all of the T5 sites have occupancies higher than 0.85; five T5 sites are fully occupied by Li, and a further seven have occupancies higher than 0.86(4). The two remaining T5 sites (1× 0.162(5)Zn/0.59(6)Li and 1× 0.031(5)Zn/ 0.21(6)Li) occupy face-sharing tetrahedra, giving a combined occupancy of 0.99(9) across both sites, analogous to the disordered environments in the high-temperature F43m structure (Figure 6c). The large number of T5 sites occupied in Li 7 Zn 0.5 SiS 6 is consistent with other ordered Li-rich argyrodites, such as Li 7 PCh 6 (Ch = S, Se), in which Li predominantly occupies tetrahedral T5 sites (six T5 sites and one T5a site). 7 None of the trigonal planar 24g (T5a) positions occupied in the high-temperature F43m structure are occupied at room temperature, reflecting the preference for a higher (tetrahedral) coordination environment for Li + in Li 7 Zn 0.5 SiS 6 . This is distinct from the low temperature (Cc) structures of Li 6 AsS 5 I and Li 6 PS 5 I and the F43m structure of Li 6 PO 5 Br, all of which contain trigonal planar T5a positions fully occupied by Li. 7,10 This is not exclusive to anion-ordered argyrodites, as fully occupied trigonal planar T5a environments are also observed in Li 7 PCh 6 (Ch = S, Se). 7 Two of the four T2 sites in Li 7 Zn 0.5 SiS 6 are fully occupied with Li at room temperature and share edges with their neighboring Li sites. The remaining two T2 sites have low occupancies (<0.09) and share faces with occupied neighboring T5 sites. The two T4 sites are both fully occupied with Li at room temperature (Figure 6c,d). The occupancy of a single T1 site at room temperature in Li 7 Zn 0.5 SiS 6 ( Figure 6c) is surprising as this position is not usually occupied in other argyrodites. Through consideration of the tetrahedral holes available for occupancy by Li in the argyrodite structure, this site is the least favorable as it shares a common face with the SiS 4 4− tetrahedra, which would result in significant repulsion from the nearby Si 4+ cation located only 2.1(2) Å away. 7 This is likely the reason the T1 site in Li 7 Zn 0.5 SiS 6 is occupied with only 0.12(3) Li, and the position is not occupied in the high-temperature F43m structure. Finally, there is one Li site that adopts trigonal planar geometry in Li 7 Zn 0.5 SiS 6 at room temperature (4e Wyckoff position), different from the commonly occupied T5a site, is not observed in other argyrodites, and like the T1 position is not occupied in the high-temperature structure. This is the trigonal face that is shared between two neighboring T2 tetrahedra, and as such, this new site is denoted as T2a. This position shares edges with one SiS 4 4− tetrahedra and two T5 Li tetrahedra, yielding a short Li− Chemistry of Materials pubs.acs.org/cm Article Li of 1.82(7) Å (Figure 6d). The combined occupancy of these positions sums to unity. 6 Li MAS NMR was utilized to obtain insights into the local structure and ordering of Li 7 Zn 0.5 SiS 6 at room temperature. The 6 Li MAS NMR spectrum recorded at room temperature ( Figure  S12b) displays a single narrow resonance at 1.65 ppm, which agrees well with all (but one) of the lithium atoms occupying tetrahedral sites. The low occupancy of the remaining single lithium in the T2a trigonal planar position among the 21 other Li sites likely limits the clear observation of this local environment in the 6 Li spectrum. It is also quite likely that the 6 Li MAS NMR spectrum is motionally averaged over all crystallographic sites due to fast Li ion hopping (see 7 Li NMR data below) and prevents spectral resolution of the two different Li local environments.
The addition of a relatively small amount of Zn 2+ (Li/Zn ratio is 14:1 in Li 7 Zn 0.5 SiS 6 ) results in the ordering observed below 411 K in the tetragonal I4 Li 7 Zn 0.5 SiS 6 structure. Argyrodites that contain more than one metal on the mobile cation sites (i.e., sharing the site with Li + ) are rare but are not unheard of. Both Al 3+ and Si 4+ occupy 48h and 16e positions alongside Li + in Li 6 3.5 Ge 1.5 P 0.5 S 6 has Ge 4+ present on both the 48h (shared with Li + ) and 4b (shared with P 5+ ) positions. 39 These three materials retain the F43m symmetry typical of argyrodites, and the additional cations (Al 3+ , Si 4+ , and Ge 4+ ) present on the Li sites in these materials do not exhibit ordering of any kind. This is distinct from Li 7 Zn 0.5 SiS 6 in which a unique ordering pattern occurs in the Zn distribution that stabilizes the roomtemperature I4 structure, explaining why only 6 of the 14 available T5 positions are occupied by Zn in the roomtemperature I4 structure. The distribution of Zn at room temperature in the I4 structure is separated into groups on the basis of Zn site occupancy. At the center of each group are four corner-connected tetrahedral sites with the highest Zn occupancy of 0.473(4) (the remainder is 0.51(5) Li) as shown in Figure 7a. Additional Zn occupied positions are located around these clusters, and Zn site occupancies decrease with an increase in distance from the group center (Figure 7a−c). These groups of Zn-rich sites are ordered to maximize the distance (15.78 Å) between neighboring groups (Figure 7a). This is distinct from the high-temperature F43m structure in which Zn is distributed throughout the structure on the disordered 48h T5 positions (Figure 7d). Though beyond the scope of the current study, this unique ordering of Zn positions in I4 Li 7 Zn 0.5 SiS 6 could be further investigated through electron microscopy, pair distribution analysis, and large-box reverse Monte Carlo modeling.
3.4. Ionic Transport in Li 7 Zn 0.5 SiS 6 . The total ionic conductivity of Li 7 Zn 0.5 SiS 6 was investigated via AC impedance spectroscopy, and local lithium ionic mobility was assessed through 7 Li solid-state NMR. AC impedance measurements were carried out on a sintered pellet of Li 7 Zn 0.5 SiS 6 of 81% theoretical density (≈30 mg of powder pressed into a 5 mm diameter pellet at a pressure of 125 MPa). A typical data set measured at 303 K under an inert Ar atmosphere is shown in Figure 8a. The impedance complex plane plots, Z*, consist of a higher-frequency arc and low frequency spike with the latter being associated with the capacitance of the sample−electrode interface that blocks the Li ions. The higher-frequency arc is attributed to the total conductivity (σ) of Li 7 Zn 0.5 SiS 6 with an associated capacitance of 0.1 pF cm −1 , corresponding to a permittivity of ≈1, consistent with the bulk response of the sample ( Figure S13). To a first approximation, this arc can be modeled with an equivalent circuit consisting of a resistor in parallel with a constant phase element (CPE) (Figure 8a (inset)). Li 7 Zn 0.5 SiS 6 presents a total conductivity of 1.0(2) × 10 −7 S cm −1 at 303 K and 4.3(4) × 10 −4 S cm −1 at 503 K. Values of total resistance were obtained in the temperature range from 303 to 503 K from the low-frequency intercept on the Z′ axis of the impedance arc and are shown in an Arrhenius plot in Figure  8b. Two separate regimes are observed, separated by a change in slope between 403 and 423 K, which coincides with the structural transition from tetragonal (I4) to cubic (F43m) symmetry observed via DSC and VT-PXRD measurements. Tetragonal Li 7 Zn 0.5 SiS 6 has an activation energy of 0.66(1) eV, while cubic Li 7 Zn 0.5 SiS 6 exhibits an activation energy of 0.34(1) eV above 423 K. Figure S14b−d shows the current−time curves of the Au|Li 7 Zn 0.5 SiS 6 |Au cell under DC polarization measured at −0.05, 0.1, and 0.7 V at which steady state current is achieved. The steady current is attributed to electronic leakage as two ionblocking electrodes were used. Such a method provides an estimation of the upper limit of the electronic conductivity. 40 The electronic conductivity (σ e ) determined from the I−E curve is 5.1(4) × 10 −10 S cm −1 at 303 K, which accounts for 0.51% of the overall conductivity, extracted through σ e = Id/EA where I is the current, d is the pellet thickness, E is the polarization voltage, and A is the electrode area.
Insights into the local Li ion mobility in tetragonal Li 7 Zn 0.5 SiS 6 were obtained through VT 7 Li solid-state NMR. Static 7 Li NMR spectra over the 140−410 K temperature range were recorded (Figure 8c) to observe the temperature dependence of the 7 Li line width. At temperatures below Chemistry of Materials pubs.acs.org/cm Article ≈175 K, 7 Li ion mobility is in the rigid lattice regime; hence, the 7 Li central transition is broadened by the strong 7 Li− 7 Li homonuclear dipolar coupling, and a line width of ≈7.5 kHz is observed. As the temperature is increased above 225 K, onset of motional narrowing (T onset ) occurs and the increased motion of the 7 Li spins continuously averages the dipolar interactions, causing the line width to decrease (Figure 8d). Using the temperature of this motional narrowing, 41 an estimation of the activation energy for the local lithium ion diffusion process of 0.4 eV is obtained for tetragonal Li 7 Zn 0.5 SiS 6 . This value is lower than that obtained through AC impedance spectroscopy (0.66(1) eV) and captures the easier local hops between neighboring Li sites while the impedance data probe longer range translational lithium ion mobility. As the temperature is increased further, the 7 Li NMR line widths continue to decrease up to >340 K where Li 7 Zn 0.5 SiS 6 is in the fast-motional regime, resulting in an averaging of the dipolar interaction and giving rise to narrow spectra with line widths of ≈750 Hz. The Li ion jump rate, τ −1 , at the temperature of the inflection point of the line narrowing curve is on the order of the central transition line width in the rigid lattice regime (≈7.5 kHz) and yields a value of 4.7 × 10 4 s −1 .
Argyrodite site hopping mechanisms that form conduction pathways for Li + ions can be categorized into three types: 8 "doublet" jumps that represent local motion between facesharing 48h (T5) sites via the trigonal planar 24g (T5a) position, "intracage" jumps between neighboring 48h (T5) tetrahedra that share edges likely facilitated by 48h (T2) tetrahedra acting as intermediate sites, and "intercage" jumps where Li + ions move between 48h (T5) sites in adjacent cages via either 48h (T2) or 16e (T4) positions, where the latter would produce a continuous face-sharing tetrahedral pathway for Li + ions (Figure 8e). These T2 and T4 positions have partial occupancy in Li 7 Zn 0.5 SiS 6 and likely form part of the extended conduction pathway. It is clear that the delocalization of lithium positions (Figure 8e) in the high-temperature cubic structure (>411 K) has a significant impact on Li ion mobility with an activation energy approximately half (0.34(1) eV) that of the room-temperature ordered tetragonal structure (0.66(1) eV). This significant decrease in activation energy between the I4 and F43m structures of Li 7 Zn 0.5 SiS 6 can be understood by considering the Li−Li site distances that become available in the hightemperature structure. The intracage distances (T5−T5 and T5−T2) are very similar between the I4 and F43m structures, while the intercage distances (represented by T5−T4 and T2− T2) are much longer in the room-temperature I4 structure of Li 7 Zn 0.5 SiS 6 (Table S7). In addition, the ordered Li sublattice in I4 Li 7 Zn 0.5 SiS 6 reduces the number of these distances, severely limiting long-range Li ion diffusion.
The room-temperature conductivity of Li 7 Zn 0.5 SiS 6 (σ 303 K = 1.0(2) × 10 −7 S cm −1 ) is low and is comparable to other ordered argyrodite materials such as Li 7 PS 6 and Li 6 PS 5 I, which have room-temperature conductivities reported in the range of 3.3 × 10 −8 to 2 × 10 −6 S cm −1 . 11,12,42−45 The conductivity in the high- Chemistry of Materials pubs.acs.org/cm Article temperature F43m regime (Li 7 Zn 0.5 SiS 6 , σ 503 K = 4.3(4) × 10 −4 S cm −1 ) is an order of magnitude higher than that of F43m Li 7 PS 6 (5.9 × 10 −5 S cm −1 ) and Li 6 PS 5 I (1.3 × 10 −5 S cm −1 ) at the same temperature. 43 This results from the more delocalized distribution of Li in the high-temperature F43m structure (Figure 8e) compared against Li 6 PS 5 I and Li 7 PS 6 in which only two sites (T5 and T5a) and one site (T5) are occupied, respectively. 7,9 Interestingly, the low temperature ordered structures of argyrodites such as Li 7 PS 6 (Pna2 1 ) and Li 6 Table S7). Related to this, the intercage T5−T4 distances are much shorter (1.643(5) Å) for Li 7 Zn 0.5 SiS 6 compared to that (1.93 Å) for Li 6.6 P 0.4 Ge 0.6 S 5 I, while the T2−T2 intercage distances are 2.11(9) Å for Li 7 Zn 0.5 SiS 6 compared to 1.93 Å for Li 6.6 P 0.4 Ge 0.6 S 5 I ( Figure  8e,f). The conductivity of F43m Li 7 Zn 0.5 SiS 6 is higher than that of other argyrodites, which show order−disorder behavior in the same regime (e.g., Li 6 PS 5 I and Li 7 PS 6 ), and although the conductivity is lower than those reported for highly disordered F43m argyrodites, Li 7 Zn 0.5 SiS 6 exhibits a comparable activation energy, indicating that Li ion mobility is similar. This can be attributed to the presence of Zn 2+ on the Li sublattice in Li 7 Zn 0.5 SiS 6 . The small subset of T5 sites occupied by Zn in I4 Li 7 Zn 0.5 SiS 6 compared to the disordered distribution across all T5 sites at higher temperatures in F43m Li 7 Zn 0.5 SiS 6 indicates that a low level of Zn 2+ mobility exists to stabilize the RT ordering. It is unlikely that Zn 2+ contributes significantly to the measured ionic conductivity of Li 7 Zn 0.5 SiS 6 as the Zn distribution is limited to T5 sites only, which implies that local mobility does not extend beyond intracage T5−T5 hops. The incorporation of Zn onto the Li sites may lead to blocking of Li i o n s a s p o s t u l a t e d f o r L i 3 . 5 G e 1 . 5 P 0 . 5 S 6 a n d Li 6 32,39,47 however, it is the presence of Zn in this concentration that leads to the occupation of the additional T2 and T4 sites that provide a large number of possible routes for Li ion mobility such that possible blocking effects become negligible. The overload of the mobile cation sites with a total cation (Li and Zn) content of 7.5 further enables the delocalization of Li sites by ensuring sufficient occupancy of the additional sites. Anion disorder in argyrodites is known to impact significantly on Li ion conductivity by influencing the energy landscape for Li + ion mobility. 5 Disorder on the anion sublattice, which can be controlled through anionic or cationic substitutions or the synthesis method, 14,48−51 yields an inhomogeneous distribution of charge density generating spatially diffuse and delocalized distributions of Li + ions, resulting in higher ionic mobility. Li 7 Zn 0.5 SiS 6 has a single cation (Si 4+ ) on the 4b position and is a single anion (S 2− only) system; however, it achieves a highly delocalized Li distribution in the F43m regime comparable to that of the highest conducting argyrodites. It is possible through additional substitution chemistry that the disordered F43m structure of Li 7 Zn 0.5 SiS 6 could be stabilized to lower temperatures or a more inhomogeneous charge density distribution could be achieved to further improve the ionic conductivity.

CONCLUSIONS
Li 7 Zn 0.5 SiS 6 , the first argyrodite with a tetragonal (I4) crystal structure has been synthesized and characterized through a combination of X-ray, neutron powder diffraction, NMR, and impedance spectroscopy. Li 7 Zn 0.5 SiS 6 is a rare example of an argyrodite with >7 mobile cations, and the incorporation of a small amount (6.7%) of Zn into the Li sublattice stabilizes a complex tetragonal superstructure of F43m argyrodites with a unique Li distribution previously unseen in these materials. At high temperatures, Li 7 Zn 0.5 SiS 6 adopts a F43m cubic argyrodite structure with simultaneous occupation of the 48h (T5), 24g (T5a), 48h (T2), and 16e (T4) sites, a unique site distribution that provides a range of possible pathways for ion hopping, yielding a higher conductivity than other Li-only materials such as Li 7 PS 6 that show order−disorder behavior. This combination of sites leads to an extensively delocalized Li distribution forming a continuous face-sharing tetrahedral pathway for Li ions that is accessible in F43m Li 7 Zn 0.5 SiS 6 . This is achieved via incorporation of Zn and overloading of the mobile cation content, which has a profound effect on the structure of Li 7 Zn 0.5 SiS 6 . This significantly impacts the Li ion conductivity and reveals how property-controlling cation ordering in argyrodites arises from compositional control. The realization of this unique ordering pattern offers new routes to tuning and further understanding the unexplored chemistries of argyrodite materials, in particular the unexpected increase in conductivity in the high-temperature disordered form compared to some lithium-only argyrodites.
Further details on the synthetic isolation and structural characterization (diffraction, NMR, Raman) of Li 7 Zn 0.5 SiS 6 , impedance results, elemental analysis (ICP), and tables of bond distances and angles in hightemperature F43m and room-temperature I4 structures (PDF) Li 7 Zn 0.5 SiS 6 powder CIF for HT structure (CIF) Li 7 Zn 0.5 SiS 6 powder CIF for RT structure (CIF) Li 7 Zn 0.5 SiS 6 RT structure only, with dummy atoms used for bond distance restraints during refinement (CIF) Chemistry of Materials pubs.acs.org/cm Article